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[[Image:Asymmetric Donation game - limit cycles.svg|160px|left | === <!--[[-->Mutualisms: cooperation between species<!--]]--> === | ||
=== | [[Image:Mutualism two-layer lattice.png|160px|left<!--|link= Mutualisms: cooperation between species-->]] | ||
''Upcoming:'' tutorial on | ''Upcoming:'' new tutorial on <!--[[Mutualisms: cooperation between species|-->''inter-species interactions''<!--]]--> in preparation. | ||
Cooperative interactions ''between'' species are the foundation of all mutualistic associations. Compared to ''within'' species interactions, the problem of cooperation is exacerbated because cooperation bestows benefits to members of another species. Mutual benefits require inter-species coordination to prevent exploitation. Here we show that in the spatial prisoner's dilemma surprisingly rich dynamics emerge with distinct dynamical domains separated by critical phase transitions, which imply arbitrarily large fluctuations and diverging spatial correlations. Most importantly, cooperative behaviour not only persists, but may result in intriguing, spontaneous symmetry breaking in the level of cooperation in each species. Evolution may favour asymmetric states that effectively separate species into cooperative producers and defecting consumers. Surprisingly, the asymmetry becomes more pronounced under more benign conditions of cooperation. | |||
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#Hauert, C., & Szabó, G. (2024) ''PNAS Nexus'' (in print). <!--'''462''' 347-360 [https://doi.org/10.1016/j.jtbi.2018.11.019 doi: 10.1016/j.jtbi.2018.11.019]--> | |||
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[[Image:Asymmetric Donation game - limit cycles.svg|160px|left|link= Asymmetric evolutionary games/Environmental feedback]] | |||
=== [[Asymmetric evolutionary games/Environmental feedback|Asymmetric evolutionary games]] === | |||
''Upcoming:'' tutorial on [[Asymmetric evolutionary games/Environmental feedback|''asymmetric evolutionary games'']]. | |||
In nature, asymmetric interactions are the norm rather than the exception, whereas for models in evolutionary game theory the opposite holds. Even individuals of the same species tend to differ in more ways than in just some strategic behaviour, and these differences inevitably result in asymmetries. For example, individuals may differ in body size, strength or agility, experience different developmental histories or availability and access to resources – all of which are likely to have some impact on the costs and benefits experienced by each individual in interactions. In general, such differences can be attributed either to the genetic makeup of an individual or its environmental conditions. Interestingly, asymmetry uncovers differences between genetic and cultural evolution that are not apparent when interactions are symmetric. | In nature, asymmetric interactions are the norm rather than the exception, whereas for models in evolutionary game theory the opposite holds. Even individuals of the same species tend to differ in more ways than in just some strategic behaviour, and these differences inevitably result in asymmetries. For example, individuals may differ in body size, strength or agility, experience different developmental histories or availability and access to resources – all of which are likely to have some impact on the costs and benefits experienced by each individual in interactions. In general, such differences can be attributed either to the genetic makeup of an individual or its environmental conditions. Interestingly, asymmetry uncovers differences between genetic and cultural evolution that are not apparent when interactions are symmetric. | ||
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#McAvoy, A. & Hauert, C. (2015) ''PLoS Comp. Biol.'' '''11'''(8): e1004349 [https://doi.org/10.1371/journal.pcbi.1004349 doi: 10.1371/journal.pcbi.1004349] | #McAvoy, A. & Hauert, C. (2015) ''PLoS Comp. Biol.'' '''11'''(8): e1004349 [https://doi.org/10.1371/journal.pcbi.1004349 doi: 10.1371/journal.pcbi.1004349] | ||
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=== [[Evolutionary graph theory]] === | |||
[[Image:Superstar graph (N=484, B=21, k=6).svg|160px|left|link=Evolutionary graph theory]] | [[Image:Superstar graph (N=484, B=21, k=6).svg|160px|left|link=Evolutionary graph theory]] | ||
New tutorial added on [[evolutionary graph theory]], which provides a formal approach to describe the spreading and fixation (or extinction) of a mutant type in structured populations. Interestingly, the fixation probabilities remain unaffected by the underlying structure for a [[Moran graphs|large class of graphs]]. However, some graphs may act either as [[Evolutionary amplifiers|amplifiers]] or [[Evolutionary suppressors|suppressors]] of selection by increasing or decreasing the fixation probabilities as compared to unstructured populations. In contrast, fixation and absorption times are very sensitive to changes in the graph structure and hence vary greatly even for graphs that leave fixation probabilities unchanged. Even though fixation times are, in general, not preserved between graphs, [[Graph symmetries|symmetries of a graph]] can at least ensure that fixation times do not depend on the initial location of the mutant. This summarizes research efforts that span over a decade, including: | New tutorial added on [[evolutionary graph theory]], which provides a formal approach to describe the spreading and fixation (or extinction) of a mutant type in structured populations. Interestingly, the fixation probabilities remain unaffected by the underlying structure for a [[Moran graphs|large class of graphs]]. However, some graphs may act either as [[Evolutionary amplifiers|amplifiers]] or [[Evolutionary suppressors|suppressors]] of selection by increasing or decreasing the fixation probabilities as compared to unstructured populations. In contrast, fixation and absorption times are very sensitive to changes in the graph structure and hence vary greatly even for graphs that leave fixation probabilities unchanged. Even though fixation times are, in general, not preserved between graphs, [[Graph symmetries|symmetries of a graph]] can at least ensure that fixation times do not depend on the initial location of the mutant. This summarizes research efforts that span over a decade, including: | ||
<div class="footnote" style="font-size:smaller"> | <div class="footnote" style="font-size:smaller"> | ||
Latest revision as of 14:15, 8 August 2024
Mutualisms: cooperation between species
Upcoming: new tutorial on inter-species interactions in preparation. Cooperative interactions between species are the foundation of all mutualistic associations. Compared to within species interactions, the problem of cooperation is exacerbated because cooperation bestows benefits to members of another species. Mutual benefits require inter-species coordination to prevent exploitation. Here we show that in the spatial prisoner's dilemma surprisingly rich dynamics emerge with distinct dynamical domains separated by critical phase transitions, which imply arbitrarily large fluctuations and diverging spatial correlations. Most importantly, cooperative behaviour not only persists, but may result in intriguing, spontaneous symmetry breaking in the level of cooperation in each species. Evolution may favour asymmetric states that effectively separate species into cooperative producers and defecting consumers. Surprisingly, the asymmetry becomes more pronounced under more benign conditions of cooperation.
- Hauert, C., & Szabó, G. (2024) PNAS Nexus (in print).
Evolutionary graph theory
New tutorial added on evolutionary graph theory, which provides a formal approach to describe the spreading and fixation (or extinction) of a mutant type in structured populations. Interestingly, the fixation probabilities remain unaffected by the underlying structure for a large class of graphs. However, some graphs may act either as amplifiers or suppressors of selection by increasing or decreasing the fixation probabilities as compared to unstructured populations. In contrast, fixation and absorption times are very sensitive to changes in the graph structure and hence vary greatly even for graphs that leave fixation probabilities unchanged. Even though fixation times are, in general, not preserved between graphs, symmetries of a graph can at least ensure that fixation times do not depend on the initial location of the mutant. This summarizes research efforts that span over a decade, including:
- McAvoy, A. & Hauert, C. (2015) J. R. Soc. Interface 12 20150420 doi: 10.1098/rsif.2015.0420
- Jamieson-Lane, A. & Hauert, C. (2015) J. Theor. Biol. 382 44-56 doi: 10.1016/j.jtbi.2015.06.029
- Lieberman, E., Hauert, C. & Nowak, M. (2005) Nature 433 312-316 doi: 10.1038/nature03204.